论文标题
迭代的差异集，解释近似和应用
Iterated differences sets, diophantine approximations and applications
论文作者
论文摘要
令$ v $为一个奇怪的真实多项式（即形式的多项式$ \ sum_ {j = 1}^\ ell a_jx^{2J-1} $）。我们利用一组迭代的差异来建立有关$ \ Mathcal r（v，ε）= \ {n \ in \ Mathbb {n} \，| \，| \ | v（n）\ | {<| {<iam \}} $ where $ \ \ | \ cdotest的距离的距离的新结果。然后，我们将新的二苯胺结果应用于厄运理论和组合学。特别是，我们获得了弱混合系统以及Furstenberg-Sárközy定理的新变体的新表征。
Let $v$ be an odd real polynomial (i.e. a polynomial of the form $\sum_{j=1}^\ell a_jx^{2j-1}$). We utilize sets of iterated differences to establish new results about sets of the form $\mathcal R(v,ε)=\{n\in\mathbb{N}\,|\,\|v(n)\|{<ε\}}$ where $\|\cdot\|$ denotes the distance to the closest integer. We then apply the new diophantine results to obtain applications to ergodic theory and combinatorics. In particular, we obtain a new characterization of weakly mixing systems as well as a new variant of Furstenberg-Sárközy theorem.
